[Math] If $\tan A+\sec A=e^x$, find $\cos A$

Question

If $\tan A+\sec A=e^x$, find $\cos A$

Here is what I've tried:

\begin{align}&\frac{\sin A}{\cos A}+\frac{1}{\cos A}&=e^x\\
\implies&\frac{1+\sin A}{\cos A}&=e^x\end{align}

Now, I've squared both sides, but, in vain. How should I continue? Am I proceeding wrong? Any help is much appreciated.

Answer 1

HINT:

As $\sec A+\tan A=e^x$

Now $\sec A-\tan A=\dfrac1{\sec A+\tan A}=?$

Can you solve for $\sec A?$

Finally $\cos A\cdot\sec A=?$